Sinajskij, E. S. On the almost Chebyshevian approximation to certain operators of the hereditary theory of elasticity. (English. Russian original) Zbl 0519.73015 J. Appl. Math. Mech. 46, 365-368 (1983); translation from Prikl. Mat. Mekh. 46, 467-471 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page MSC: 74B99 Elastic materials 41A50 Best approximation, Chebyshev systems 45P05 Integral operators 41A10 Approximation by polynomials 45D05 Volterra integral equations 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) Keywords:almost Chebyshevian approximation; resolvent hereditary operator; Abel or Rzhanitsyn kernel; approximated on arbitrary, finite time interval; polynomial in fractional powers; variable with exponential cofactor; smallest error in defining equation; approaches asymptotically with increasing order the Chebyshev polynomials to function on segment; error decreases with increasing order of approximation Citations:Zbl 0515.73026; Zbl 0309.41004; Zbl 0074.105 PDFBibTeX XMLCite \textit{E. S. Sinajskij}, J. Appl. Math. Mech. 46, 365--368 (1982; Zbl 0519.73015); translation from Prikl. Mat. Mekh. 46, 467--471 (1982) Full Text: DOI References: [1] Rabotnov, Iu. N., Elements of Hereditary Mechanics of Solids (1977), Nauka: Nauka Moscow [2] Rzhanitsyn, A. R., Theory of Creep (1968), Stroiizdat: Stroiizdat Moscow [3] Dziadyk, V. K., Approximation method of using the algebraic polynomials to approach the solutions of linear differential equations, (Ser. matem., Vol. 38 (1974), Izv. Akad. Nauk SSSR), No. 4 [4] Lancosz, C., Applied Analysis (1957), Pitman: Pitman London [5] Gromov, V. G., On the problem of solving boundary value problems of the linear viscoelasticity, Mekhanika polimerov., No. 6 (1967) [6] Bernshtein, S. N., Extremal Properties of Polynomials (1937), Gl.Red.obshchetekhn. lit-ry: Gl.Red.obshchetekhn. lit-ry Leningrad — Moscow · Zbl 0056.06001 [7] Jahnke, E.; Emde, F.; Lösch, F., Special Functions (1964), Nauka: Nauka Moscow [8] Sinaiskii, E. S., On the uniform approximation to the functions of Mittag—Leffler type by means of the polynomials on a segment (1980), Izv. vuzov. Matematika, No. 4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.